%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% File:               best_response.m
%
% Authors:            Sergio Ascencio and Miguel Rueda
%
% Language:           MATLAB R2013b (8.2.0.701) 64 Bit
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


function psi=best_response(betas,X,phats)

%Extended
% varsx={'l_d_RC_others' 'l_margin' 'lcasillas' 'school_ic' 'l_diff_PRI_PAN' 'lpop' 'l_turnout' 'local' 'ldist_city' ...
% 'l_d_RC_others_sq' 'l_margin_sq' 'lcasillas_sq' 'school_ic_sq' 'l_diff_PRI_PAN_sq' 'lpop_sq' 'l_turnout_sq' 'ldist_city_sq' ...
% 'l_d_RC_others_l_margin' 'l_d_RC_others_lcasillas' 'l_d_RC_others_school_ic' 'l_d_RC_others_l_diff_PRI_PAN' 'l_d_RC_others_lpop' 'l_d_RC_others_l_turnout' 'l_d_RC_others_local' 'l_d_RC_others_ldist_city' ...
% 'l_margin_lcasillas' 'l_margin_school_ic' 'l_margin_l_diff_PRI_PAN' 'l_margin_lpop' 'l_margin_l_turnout' 'l_margin_local' 'l_margin_ldist_city' ...
% 'lcasillas_school_ic' 'lcasillas_l_diff_PRI_PAN' 'lcasillas_lpop' 'lcasillas_l_turnout' 'lcasillas_local' 'lcasillas_ldist_city' ...
% 'school_ic_l_diff_PRI_PAN' 'school_ic_lpop' 'school_ic_l_turnout' 'school_ic_local' 'school_ic_ldist_city' ...
% 'l_diff_PRI_PAN_lpop' 'l_diff_PRI_PAN_l_turnout' 'l_diff_PRI_PAN_local' 'l_diff_PRI_PAN_ldist_city' ...
% 'lpop_l_turnout' 'lpop_local' 'lpop_ldist_city' ...
% 'l_turnout_local' 'l_turnout_ldist_city' ...
% 'local_ldist_city' 'ldist_pri' 'gov_PRI' 'ldist_pan' 'gov_PAN'};

psi=cell(1,2);

p_PRI=phats{1,1}(:,1:2); %remember prob H in first, M in second column
p_PAN=phats{1,2}(:,1:2);


    Z_PAN=X(:,end-1:end);
    Z_PRI=X(:,end-3:end-2);
    X=X(:,1:9);

%Base outcome is L (minimum representation)
betas_PRI=[zeros(size(betas,1),1) betas(:,1:2)];
betas_PAN=[zeros(size(betas,1),1) betas(:,3:4)];

X_PRI=[X Z_PRI p_PAN ones(size(X,1),1)];
X_PAN=[X Z_PAN p_PRI ones(size(X,1),1)];

psi_PAN=exp(X_PAN*betas_PAN)./kron(ones(1,3),sum(exp(X_PAN*betas_PAN),2));
psi_PRI=exp(X_PRI*betas_PRI)./kron(ones(1,3),sum(exp(X_PRI*betas_PRI),2));

psi{1,2}=[psi_PAN(:,3) psi_PAN(:,2) psi_PAN(:,1)];
psi{1,1}=[psi_PRI(:,3) psi_PRI(:,2) psi_PRI(:,1)]; %changing order to make it compatible with phats

end

